ALGEBRA: Mathematical Operations With Algebraic Terms - Addition

LESSON 7 

ALGEBRA: Use of Letters in Mathematics

MATHEMATICAL OPERATIONS WITH ALGEBRAIC TERMS

Mathematical operations are the basic operations carried out in mathematics. Examples are multiplication (x), division (÷), addition (+), subtraction (-) e.t.c.

We are going to discuss the addition and subtraction of algebraic terms in this lesson. Let’s go! 

ADDITION AND SUBTRACTION OF ALGEBRAIC TERMS   

Let’s start with addition of simple algebraic terms

EXAMPLE 1

Simplify a + a + a

SOLUTION

a + a + a = 3a

NOTE

1.     2 + 2 + 2 = 3 x 2 (3 times of 2) compare to a + a + a =3 x a (3 times of a)

2.     In algebra, the number that multiplies a letter is called coefficient while the letter is called the variable. Therefore

(i) In 3a, 3 is the coefficient and a is the variable

(ii) In ¾ a, ¾ is the coefficient and a is the variable 

(iii) In -2x, -2 is the coefficient and x is the variable

(iv) In p, 1 is the coefficient and p is the variable.

Did you understand this? Go over it again and be sure!  

   

EXAMPLE 2

Simplify 3x + 2x

SOLUTION

3x + 2x = (x + x + x) + (x + x)  That is (3 times of x) + (2 times of x)

             = x + x + x + x + x

             = 5x (5 times of x)  

OR

3x + 2x = (3 +2)x

             = 5x

EXAMPLE 3

Simplify 4p + 6p

SOLUTION

4p + 6p = (p + p + p + p) + (p + p + p + p + p + p)

             = p + p + p + p + p + p + p + p + p + p

             = 10p

OR

4p + 6p = (4 + 6)p

             = 10p 

LET’S PUSH IT IN!

Give quick answers to the following questions and write them in your pad.

(i) What is the coefficient of -10p?

(ii) What is the simplified form of x + x?

(iii) What is the simplified form 5q + 3q?

Check if your answers are the same as

(i) -10 (ii) 2x (iii) 8q

If they all the same as your answer, go to the ACTIVITY, if not back to the examples again!

ACTIVITY

Simplify the following

1. p + 2p

2. 4b + 4b

3. x + 9x

4. 5g + 9g

5. 5y + 13y + 2y

Post the solution as a COMMENT to this lesson. Include your name or nickname and email because every COMMENTS will be replied. I’m expecting your COMMENT.

Congratulation! You've completed this lesson. Now let's go to LESSON 8: MATHEMATICAL OPERATIONS WITH ALGEBRAIC TERMS – SUBTRACTION.

ALGEBRA: Mathematical Operations with Algebraic Terms

LESSON 5

ALGEBRA: Use of Letters in Mathematics

MATHEMATICAL OPERATIONS WITH ALGEBRAIC TERMS

Mathematical operations are the basic operations carried out in mathematics. Examples are multiplication (x), division (÷), addition (+), subtraction (-) e.t.c.

We are going to discuss the multiplication of algebraic terms in this lesson. Let’s go!

MULTIPLICATION OF ALGEBRAIC TERMS

Multiplication of algebraic terms is done by first multiplying all the numbers and then the letters. Let’s look at some examples.

EXAMPLE 1

Simplify 6a X 3

SOLUTION

6a X 3 = 3 X 6 X a          NOTE: the numbers are arranged and multiplied first.

           = 18 X a

           = 18a

EXAMPLE 2

Simplify 2 X 3y

SOLUTION

2 X 3y = 2 X 3 X y

           = 6 X y

           = 6y

EXAMPLE 3

Simplify 5b X 4c

SOLUTION

5b X 4c = 5 X 4 X b X c

             = 20 X b X c

             = 20 X bc

             = 20bc

EXAMPLE 4

Simplify 7a X 3a

SOLUTION

7a X 3a = 7 X 3 X a X a

             = 21 X a X a

             = 21 X a²

             = 21a²

NOTE:        a + a = 2a    but     a X a = a²

EXAMPLE 5

Simplify 6b X 4bc

SOLUTION

6b X 4bc = 6 X 4 X b X b X c

               = 24 X b X b X c

               = 24 X b² X c

               = 24 X b²c

               = 24b²c

PUSH IT IN!

Go over the examples again. Write the questions down in your note pad and attempt solving them without looking at the examples.

 Did you get them? 

Yes? Good! Now go to the activity.

No? Good. There are some little misunderstandings here. Let’s solve it together. Send me a COMMENT!

ACTIVITY

Simplify the following

1. 4p X 7
2. 3y² X 4
3. P X 2q
4. 5n X 7n
5. 14pq X p

Post the solution as a COMMENT to this lesson. Include your name or nickname and email because every COMMENTS will be replied. I’m expecting your COMMENT.

Congratulation! You've completed this lesson. Now let's go to LESSON 6: MATHEMATICAL OPERATIONS WITH ALGEBRAIC TERMS – DIVISION

ALGEBRA: Mathematical Operations with Algebraic Terms- Division

LESSON 6

ALGEBRA: Use of Letters in Mathematics

MATHEMATICAL OPERATIONS WITH ALGEBRAIC TERMS

Mathematical operations are the basic operations carried out in mathematics. Examples are multiplication (x), division (÷), addition (+), subtraction (-) e.t.c.

We are going to discuss the division of algebraic terms in this lesson. Let’s go! 

DIVISION OF ALGEBRAIC TERMS

Division of algebraic terms is done by dividing the numbers in the numerator by numbers in the denominators and then doing the same to the letters. Let’s look at some examples.

EXAMPLE 1

Simplify 16h ÷ 4

SOLUTION

16h ÷ 4 = 16 X h

                    4

             = 4 X h

                   1

            = 4h

EXAMPLE 2

Simplify 3cd ÷ d

SOLUTION

3cd ÷ d = 3 X c X d

                      d

              = 3 X c X 1

                       1

                  

              = 3c

EXAMPLE 3

Simplify

8ab

2a

SOLUTION

8ab  =  8 X a X b

2a           2 X a

       =  4 X 1 X b

               1 X 1

                     

       = 4b

EXAMPLE 4

Simplify 36e²f ÷ 9ef

SOLUTION

36e²f ÷ 9ef = 36 X e X e X f

                        9 X e X f

                  = 4 X e X 1

                     1 X 1 X 1

                  = 4e

PUSH IT IN!

Simplify the divisions in the examples in your pad without looking at the solutions.

Did you get them correctly? Good, now go to the activities.

If you cannot simplify any of the examples without looking at the solution, tell me about the problem in a COMMENT and let’s solve it together.

ACTIVITY

Simplify the following

1.  28ab ÷ 4

2.  6mn ÷ 3m

3.  15c²

      5c

4.  81qp²

      3p

Post the solution as a COMMENT to this lesson. Include your name or nickname and email because every COMMENTS will be replied. I’m expecting your COMMENT.

Congratulation! You've completed this lesson. Now let's go to LESSON 7: MATHEMATICAL OPERATIONS WITH ALGEBRAIC TERMS – ADDITION AND SUBTRACTION.